Trigonometric Limit Problem: Finding the Limit as x Approaches 0

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To find the limit as x approaches 0 of 3sin(4x) / sin(3x), the key is to apply the limit property lim as x -> 0 of sin(x)/x = 1. By rewriting sin(4x) as 2sin(2x)cos(2x) and manipulating the expression, the problem simplifies to a well-known limit. After applying the appropriate trigonometric identities and limits, the solution becomes straightforward. This approach effectively demonstrates the use of fundamental trigonometric limits in calculus. The final limit can be easily computed once the expression is simplified correctly.
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Homework Statement


find the limit as x approaches 0 of 3sin4x / sin3x


Homework Equations


sin2x = 2sinxcosx
lim as x ->0 of sinx / x =1


The Attempt at a Solution


sin4x = 2 sin2x cos2x
 
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Divide and multiply both numerator and denominator with the angles of resective sin .
You will get one famous limit , after that its a breeze :cool:
 

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